Notes on Minimax, Maximin and Maximax
Essay by avn19 • April 22, 2018 • Study Guide • 404 Words (2 Pages) • 952 Views
Notes on Maximin, Maximax and Minimax (Regret criterion)
- Used when probabilities of events are unknown
- Based on the attitude of the investor
Maximin
- Investors aim to maximise minimum return, hence the name Maximin.
- Under this method the decision maker assumes the worst possible outcome and hopes to maximise that outcome, thus chooses the largest pay-out under the “worst” circumstances
- It is a pessimistic approach
Maximax
- It is a more optimistic approach
- Investors seek to maximise the maximum return hence the name Maximax.
- Under this method decision maker will assume the best outcome and seek to maximise it
Minimax or Regret Criterion
- This is a more neutral approach
- Under this approach the decision maker simply aims to minimise maximum regret hence the name minimax.
- This regret could be defined as the financial gain between different outcomes, and can be identified using opportunity costing
Example
Peter is a budding entrepreneur who is interested in starting a one of a kind digital technology business, he is torn between two high end machines that he could possibly use. however due to a lack of such firms in the market, the uncertainties that would affect the demand of the service is difficult to predict. The following are the possible outcomes
Recommend a decision based on the use of the Maximin, Maximax and regret criteria approaches.
Income generated by the use of machines under different events
High demand ($) | Low Demand ($) | |
Machine A | 100,000 | 70,000 |
Machine B | 250,000 | 10,000 |
Under Maximin, the decision maker here Peter will assume the worst outcome will occur and try to maximise the return of such a situation, thus under low demand
Assuming low demand, he sees that
Machine A shall provide a turnover of $70,000 and Machine B a turnover of $10,000
Peter shall choose to use Machine A
Under Maximax, the decision maker here Peter will assume the best outcome will occur and try to maximise the return of such a situation, thus under high demand
Assuming high demand, he sees that
Machine A shall provide a turnover of $100,000 and Machine B a turnover of $250,000
Peter shall choose to use Machine B
Under Minimax, the decision maker here Peter will try to minimise maximum regret.
To do this we must make a regret table by looking at the initial schedule
High demand ($) | Low Demand ($) | |
Machine A | 100,000 | 70,000 |
Machine B | 250,000 | 10,000 |
Regret Table | High Demand | Low Demand | Maximum Regret |
Machine A | 150,000 | 0 | 150,000 |
Machine B | 0 | 60,000 | 60,000 |
Under this Peter would want to minimise his maximum regret so he would choose to go with Machine B as the maximum regret is lower than the regret of choosing Machine A.
...
...